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A concave mirror has a focal length of 5.00 cm. Using the mirror equation, what is the image distance for an object placed 7.00 cm from the mirror?
A-17.5 cm
B2.92 cm
C-2.92 cm
D17.5 cm
Answer & Solution
Correct answer: D. 17.5 cm
1. The mirror equation is 1/f = 1/d_i + 1/d_o, so 1/d_i = 1/f - 1/d_o.
2. Substituting f = 5.00 cm and d_o = 7.00 cm gives 1/d_i = 1/5.00 - 1/7.00.
3. Using a common denominator of 35, this is 7/35 - 5/35 = 2/35 per cm.
4. Inverting gives d_i = 35/2 = 17.5 cm.
5. The positive sign shows the image is real, consistent with an object placed beyond the focal length of a concave mirror.
6. A negative value such as -17.5 cm would wrongly describe a virtual image, which does not apply here.
7. 2.92 cm and -2.92 cm both come from mishandling the fraction subtraction rather than combining the two reciprocals correctly.
_Source: OpenStax Physics (CC BY 4.0), Ch 16 "Mirrors and Lenses", section 16.1 Reflection_
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